x^2-5x=3(x-5)

Solution for x^2-5x=3(x-5) equation:

Simplifying
x2 + -5x = 3(x + -5)

Reorder the terms:
-5x + x2 = 3(x + -5)

Reorder the terms:
-5x + x2 = 3(-5 + x)
-5x + x2 = (-5 * 3 + x * 3)
-5x + x2 = (-15 + 3x)

Solving
-5x + x2 = -15 + 3x

Solving for variable 'x'.

Reorder the terms:
15 + -5x + -3x + x2 = -15 + 3x + 15 + -3x

Combine like terms: -5x + -3x = -8x
15 + -8x + x2 = -15 + 3x + 15 + -3x

Reorder the terms:
15 + -8x + x2 = -15 + 15 + 3x + -3x

Combine like terms: -15 + 15 = 0
15 + -8x + x2 = 0 + 3x + -3x
15 + -8x + x2 = 3x + -3x

Combine like terms: 3x + -3x = 0
15 + -8x + x2 = 0

Factor a trinomial.
(3 + -1x)(5 + -1x) = 0

Subproblem 1
Set the factor '(3 + -1x)' equal to zero and attempt to solve:

Simplifying
3 + -1x = 0

Solving
3 + -1x = 0

Move all terms containing x to the left, all other terms to the right.

Add '-3' to each side of the equation.
3 + -3 + -1x = 0 + -3

Combine like terms: 3 + -3 = 0
0 + -1x = 0 + -3
-1x = 0 + -3

Combine like terms: 0 + -3 = -3
-1x = -3

Divide each side by '-1'.
x = 3

Simplifying
x = 3
Subproblem 2
Set the factor '(5 + -1x)' equal to zero and attempt to solve:

Simplifying
5 + -1x = 0

Solving
5 + -1x = 0

Move all terms containing x to the left, all other terms to the right.

Add '-5' to each side of the equation.
5 + -5 + -1x = 0 + -5

Combine like terms: 5 + -5 = 0
0 + -1x = 0 + -5
-1x = 0 + -5

Combine like terms: 0 + -5 = -5
-1x = -5

Divide each side by '-1'.
x = 5

Simplifying
x = 5
Solution
x = {3, 5}